The Tesla was originally invented by Nikola Tesla, but when Claudia Donovan became an agent she made one herself. Originally, Teslas could only fire one to two times between charges, depending on their setting. Once they run out of power, the Teslas would have to be returned to their carrying case, where they could be plugged in and recharged by some as-yet unexplained means. Claudia discovered a way of creating a self-charging system for the Teslas, as well as miniaturizing the Tesla for better concealment.
In the episode "The Ones You Love" it is revealed that Claudia made Agent Jinks his own mini-Tesla, which is gifted to him by Mrs. Frederic.